Parking in Galveston isn't too bad. The Port Authority offers parking but you need to drop off one of your family members at the pier. They take all of the bags while you go park the car. You then ride a shuttle back to the pier. This means you sit through the line of cars twice. The same is true when you return. You ride the shuttle to get the car while a family member waits with the luggage. I have done this on many cruises from Galveston and have found that a private company named Dolphin Parking is much easier. There lot is right next to the Port Authority lot. There lot has some spaces with blue canopys for covered parking. You stop in there, pay your fee(about $9 a day) then you and the family with your luggage are shuttled to the pier drop off. When you return, you all ride back to the parking lot together. Hope this helps. Remember look for the blue canopy's on the right side as you get close to the pier.
I posted this somewhere else but I'll mention it again. The parking in Galveston is not something you really want to do unless you have no alternative. However, you might think about what I did. I left my car at a Toyota dealership to have some routine maintenance done, they dropped us all off at the pier (baggage and all)and picked us up on our return (called on our cell phone).
I basically got free parking, dropoff and pickup service at no charge, and to make it all even better, there was an internet 10% coupon for routine service! Not a bad deal at all.
We have had good experienced each of the three times we've parked in Galveston. The dolphin lot (used 2x's) is the best, but we also used EZ Cruise Parking and it was pretty good. EZ is close enough to the peir we walked back to the car with our luggage instead of waiting for a shuttle. Dolphin is better about providing plenty of large shuttle busses so the wait is minimal. I've heard the "official lot" is a nightmare though, but can't say myself, as I've never used it.
Like the above poster, we cruised the Grand in Nov. and will be sailing her again Apr. 9th and we will be parking in the Dolphin lot.
I decided to book a hotel right on the Ocean for less money to pay to park. They said I can leave the car there for the week. This worked out great since I was already going to look for a budget hotel around Galveston since I am driving from Dallas (Did not want to risk driving on the same day). I am now staying in a nice hotel on the beach. Thanks Paul for the advice on that one and thanks everyone else for the great suggestions.